The present invention generally relates to phase shifter arranging methods and computer program products, and more particularly to a phase shifter arranging method for arranging phase shifters with respect to a photomask, and to a computer program product which stores a program for carrying out the phase shifter arranging method.
Recently, patterns of semiconductor integrated circuits have become smaller, and there are demands to improve the focal depth and the resolution of the exposure.
An amplitude of monochromatic light transmitted through aperture patterns 2 and 4 of a photomask 1 shown in FIG.1A and an amplitude of monochromatic light transmitted through aperture patterns 3 and 5 of the photomask 1 respectively become as indicated by .o slashed.1 and .o slashed.2 on a semiconductor waver, as shown in FIG.1B. In the case, a light intensity becomes proportional to .vertline..o slashed.1+.o slashed.2.vertline..sup.2 as shown in FIG.1C. The lights transmitted through the aperture patterns 2 through 5 are diffracted, and interfere so as to intensify each other between the adjacent exposure patterns, thereby causing the resolution of the exposure to deteriorate. This problem of deteriorating resolution of exposure becomes more conspicuous as the patterns become smaller.
Hence, as shown in FIG.1D, there is a technique to eliminate the above described problem by arranging phase shifters (or phase shift layers) 6 and 7 over the corresponding aperture patterns 3 and 5 of a photomask 1A. In this case, the lights transmitted through adjacent aperture patterns have a phase difference of .pi.radians, so that the transmitted lights interfere so as to weaken each other. The monochromatic light transmitted through the aperture patterns 3 and 5 has an amplitude -.o slashed.2 shown in FIG.1E. In addition, the light intensity becomes proportional to .vertline..o slashed.1-.o slashed.2.vertline..sup.2 as shown in FIG.1F. Hence, the resolution of the exposure is improved and the focal depth is also improved by the provision of the phase shifters 6 and 7.
A large number of aperture patterns are arranged two-dimensionally on the photomask. In general, it is therefore impossible to arrange the phase shifter on only one of the two mutually adjacent aperture patterns with respect to all of the mutually adjacent aperture patterns. In addition, when 1000 aperture patterns exist, for example, there are 2999 different ways to arrange the phase shifters, and it is difficult even by use of a computer to find an optimum solution.
Conventionally, a skilled person determined the arrangement of the phase shifters manually. As a result, the operation of determining the arrangement of the phase shifters was extremely complex and troublesome to carry out, thereby putting a large burden on the skilled person. In addition, it was difficult to find a desirable or optimum arrangement for the phase shifters. It is conceivable to use a computer to arrange the phase shifters at random and then optimize this random arrangement, however, there is just too many ways to arrange the phase shifters, and this conceivable method is impractical.
Therefore, it was more practical for the skilled person to manually determine the arrangement of the phase shifters.